Baking soda! And vinegar!
Sprinkle baking soda on dirty sill and work it with a brush until it has worked all the dirt you can loose. Especially into corners and crevices. An old denture brush works very well for this job. I use this old denture brush for many cleaning chores.
Step 2. vacuum up dry baking soda and dirt.
Step 3. Spray cleaner with vinegar or straight vinegar, in corners especially and let it bubble a bit. Wipe clean!
I was amazed how well this worked.